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Stress Analysis of Thin Metal Construction

Published online by Cambridge University Press:  28 July 2016

H. L. Cox
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Extract

In seeking to analyse the stress distribution in a complex structure, our object is really twofold. In the first place, if the stress in each part is accurately known, the strength of each part separately can be assessed on the basis of tests on simple units and the necessity for testing the complete structure may be avoided. In the second place, if the stress distribution can be expressed as a function of the geometry of the structure, the effect of varying that geometry, particularly with the object of realising Holmes’ one-hoss-shay, can be examined theoretically and arbitrary-features of the design can be eliminated. If our knowledge were complete, any structure designed to a maximal or minimal condition would not permit any variation from one ideal form, the design would be uniquely determined by the stated requirements.

Type
Proceedings
Information
The Aeronautical Journal , Volume 44 , Issue 351 , March 1940 , pp. 231 - 282
Copyright
Copyright © Royal Aeronautical Society 1940

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References

References

I. General

(a) Theory

(b) Practical

II. Flat Panels

(a) Theory of Buckling

(i) Compression

(ii) Shear

(b) Behaviour after Buckling and Strength

(i) Compression

(ii) Shear

III. Curved Panels

(a) Theory of Buckling

(i) Compression

(ii) Shear

(b) Behaviour after Buckling and Strength

(i) Compression

(ii) Shear

IV. Tubes

(a) Theory of Buckling

(i) Compression and Bending

(ii) Torsion

(b) Behaviour after Buckling and Strength

(i) Compression

(ii) Bending

(iii) Torsion

(iv) Combined Bending and Shear

V. Strength of Stiffeners

VI. Stability Under Compression of Combinations of Stiffeners and Panels

(a) Theoretical

(b) Experimental

VII. Stability of Corrugated and Orthotropic Panels

(a) Theoretical

(b) Experimental

VIII. Stability of Orthotropic Cylinders

IX. Stiffening of Holes Cut in Monocoque Structure

X. Diffusion of Concentrated Loads into Monocoque Structure

XI. Rivets

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9. Southwell, R. V.. On the Analysis of Experimental Observations in Problems of Elastic Stability. Proc. Roy. Soc. A., Vol. 135, p. 601.Google Scholar
10. Bryan, G. H.. On the Stability of a Plane Plate under Thrust. Proc. Lond. Math. Soc., Series 1, Vol. 22, p. 54.Google Scholar
11. Taylor, G. I.. The Buckling Load of a Rectangular Plate with Four Clamped Edges. Z.A.M.M. 13, p. 147.Google Scholar
12. Faxen, H.. Buckling of a Rectangular Plate. Z.A.M.M. 15, p. 268.Google Scholar
13. Weinstein, A.. On a Minimal Problem in the Theory of Elasticity. Jour. Lond. Math. Soc., Vol. 10, p. 184.Google Scholar
14. Trefftz, E.. The Estimation of the Buckling Load of a Rectangular Plate under Compression. Z.A.M.M. 15, p. 339.Google Scholar
15. Southwell, R. V. and Skan, S. W.. On the Stability under Shearing Forces of a Flat Elastic Strip. Proc. Roy. Soc. A., Vol. 105, p. 582.Google Scholar
16. Gough, H. J. and Cox, H. L.. Some Tests on the Stability of Thin Strip Material under Shearing Forces in the Plane of the Strip. Proc. Roy. Soc. A., Vol. 137, p. 145.Google Scholar
17. Aldous, C. W., Cox, H. L. and Gough, H. J.. The Strength of Panel Bracing. A.R.C. Techl. Rep. No. 3029 (unpublished).Google Scholar
18. Cox, H. L.. The Buckling of Thin Plates in Compression. A.R.C, R. & M. No. 1554.Google Scholar
19. Kármán, Th. V.. The Strength of Thin Plates in Compression. C.I.T. Pub. No. 13.Google Scholar
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21. Sechler, E. E.. The Ultimate Strength of Thin Flat Sheets in Compression. C.I.T. Pub. No. 27.Google Scholar
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25. Kuhn, P.. A Summary of Design Formulae for Beams having Thin Webs in Diagonal Tension. N.A.C.A. Techl. Note No. 469.Google Scholar
26. Atkin, E. H.. Stiffness in Stressed Skins. Aircraft Engineering, Vol. 8, p. 213.CrossRefGoogle Scholar
27. Schapitz, E.. Contributions to the Theory of the Incomplete Tension Bay. L.F.F. 14, p. 129.Google Scholar
28. Redshaw, S. C.. Elastic Stability of a Curved Plate under Axial Thrust. J.R.Ae.S., Vol. 42, p. 536.Google Scholar
29. Leggett, D. M. A.. The Elastic Stability of a Long Slightly Bent Rectangular Plate under Uniform Shear. Proc. Roy. Soc. A., Vol. 162, p. 62.Google Scholar
30. Sechler, E. E.. Preliminary Report on the Ultimate Compressive Strength of Curved Panels. C.I.T. Pub. No. 36.Google Scholar
31. Cox, H. L. and Clenshaw, W. J.. Compression Tests on Curved Panels of Thin Sheet Duralumin. A.R.C. Techl. Rep. No. 1576 (unpublished).Google Scholar
32. Marguerre, K.. On the Strength of Shells of Small Curvature. Proc. 5th Int. Cong. App. Mechanics. (See also Ref. 8.)Google Scholar
33. Smith, G. M.. Strength in Shear of Thin Curved Sheets of Alclad. N.A.C.A. Techl. Note No. 343.Google Scholar
34. Wagner, H. and Ballerstedt, W.. Fields of Tension Stress in Thin Plates, Initially Curved, under Shear Load. L.F.F. 12, p. 70.Google Scholar
35. Chwalla, E.. Collapse of Tubes under End Thrust. Z.A.M.M. 10, p. 72.Google Scholar
36. Donnell, L. H.. A New Theory for the Buckling of Thin Cylinders under Axial Compression'and Bending. A.S.M.E., AER-56-12.Google Scholar
37. Brazier, L. G.. The Flexure of Thin Cylindrical Shells and other Thin Sections. A.R.C, R. & M. No. 1081. (See also Ref. 2.)Google Scholar
38. Schwerin, E.. Torsional Stability of Thin-Walled Tubes. Z.A.M.M., Vol. 5, p. 235.Google Scholar
39. Donnell, L. H.. Stability of Thin-Walled Tubes under Torsion. N.A.C.A. Techl. Rep. 479.Google Scholar
40. Southwell, R. V.. On the Torsion of Conical Shells. Proc. Roy. Soc. A., Vol. 163, p. 337.Google Scholar
41. Robertson, A.. The Strength of Tubular Struts. Proc. Roy. Soc. A., Vol. 121, p. 558.Google Scholar
42. Lundquist, E. E.. Strength Tests of Duralumin Cylinders in Compression. N.A.C.A. Techl. Rep. No. 473.Google Scholar
43. Lundquist, E. E.. Strength Tests of Duralumin Cylinders in Pure Bending. N.A.C.A. Techl. Note No. 479.Google Scholar
44. Lundquist, E. E. and Burke, W. F.. Strength Tests of Thin-Walled Duralumin Cylinders of Elliptic Section. N.A.C.A. Techl. Note No. 527. (See also Ref. 4.)Google Scholar
45. Robertson, A. and Newport, A. J.. Torsion of Metal Tubes. III. Elastic Instability of Thin Tubes. A.R.C. Techl. Rep. No. 28.Google Scholar
46. Lundquist, E. E.. Strength Tests of Thin-Walled Duralumin Cylinders in Torsion. N.A.C.A. Techl. Note No. 427.Google Scholar
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48. Lundquist, E. E.. Strength of Thin-Walled Duralumin Cylinders in Combined Transverse Shear and Bending. N.A.C.A. Techl. Note No. 523. (See also Ref. 4.)Google Scholar
49. Trayer, G. W. and March, H. W.. Elastic Instability of Members having Sections common in Aircraft Construction. N.A.C.A. Techl. Rep. No. 382Google Scholar
50. Wagner, H. and Pretschner, W.. Torsion and Buckling of Open Sections. N.A.C.A. Techl Mem. No. 784.Google Scholar
51. Parr, W. S. and Beakley, W. M.. An Investigation of Duralumin Channel Section Struts under Compression. J. Aero. Sci., Vol. 3, p. 21.Google Scholar
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53. Taylor, J. L.. Stability of a Monocoque in Compression. A.R.C, R. & M. 1679.Google Scholar
54. Cox, H. L. and Smith, H. E.. The Buckling of Grids of Stringers and Ribs. A.R.C. Techl. Rep. No. 2731. (To be published.)Google Scholar
55. Cox, H. L. and Clenshaw, W. J.. The Buckling of Combinations of Sheet and Stringers. A.R.C. Techl. Rep. No. 1586 (unpublished).Google Scholar
56. Lundquist, E. E.. Comparison of Three Methods for Calculating the Compressive Strength of Flat and Slightly Curved Sheet and Stringer Combinations. N.A.C.A. Techl. Note No. 455.Google Scholar
57. Newell, J. S. and Gale, W. H.. Report on Aircraft Materials Research at Massachusetts Institute of Technology, 1930–31.Google Scholar
58. Gerard, I. J. and Dickens, B. G.. Stressed Skin Structures. Compression Tests of Panels with Tubular Stiffeners. A.R.C, R. & M. No. 1830.Google Scholar
59. Ramberg, W., McPherson, A. E. and Levy, S.. Experimental Study of Sheet Stringer Panels under End Compression. Proc. 5th Int. Cong. App. Mech.Google Scholar
60. Dean, W. R.. The Elastic Stability of a Corrugated Plate. Proc. Roy. Soc. A., Vol. III , p. 144. (See also Ref. 53.)Google Scholar
61. Bergmann, S. and Reissner, H.. The Buckling of Corrugated Sheet in Shear. Z.F.M. 20, p. 475.Google Scholar
62. Seydel, E.. Buckling Tests of Panels of Corrugated Sheet. J.D.V.L. 1931, p. 233.Google Scholar
63. Greene, C. F. and Brown, C. G.. The Column Properties of Corrugated Aluminium Alloy Sheet. A.C.I.C. No. 699. (U.S. Army Air Corps.)Google Scholar
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65. Cox, H. L.. Stiffening of Webs containing Holes. A.R.C. Techl. Rep. No. 2158 (unpublished).Google Scholar
66. Gurney, C.. An Analysis of the Stresses in a Flat Plate with a Reinforced Circular Hole under Edge Forces. A.R.C, R. & M. No. 1834.Google Scholar
67. Schüssler, K.. Sheet Strip with Bedded Circular Holes in Shear. L.F.F. 11, p. 74.Google Scholar
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69. Mathar, J.. The Resistance to Shear and Buckling of Thin Plates with Lightening Holes. Proc. Aero. Inst., Aachen, 1929.Google Scholar
70. Cox, H. L., Smith, H. E. and Conway, C. G.. Diffusion of Concentrated Loads into Monocoque Structures. A.R.C, R. & M. No. 1780.Google Scholar
71. Duncan, W. J.. Diffusion of Load in Certain Sheet-Stringer Combinations. A.R.C, R. & M. No. 1825.Google Scholar
72. Smith, H. E.. Diffusion of Load in Sheet-Stringer Combinations having a Tapered Centre Stringer. A.R.C, R. & M. No. 1862.Google Scholar
73. Cox, H. L.. Diffusion of Concentrated Loads into Monocoque Structure. General Considerations with particular reference to Bending Load Distributions. A.R.C, R. & M. No. 1860.Google Scholar
74. Winny, H. F.. The Distribution of Stress in Monocoque Wings. A.R.C, R. & M. No. 1756.Google Scholar
75. Reissner, E.. On the Problem of Stress Distribution in Wide Flanged Box Beams. J. Aero. Sci., Vol. 5, p. 295.Google Scholar
76. Lovett, B. B. C. and Rodee, W. F.. Transfer of Stress from Main Beams to Intermediate Stiffeners in Metal Sheet covered Box Beams. J. Aero. Sci., Vol. 3, p. 426.Google Scholar
77. White, R. J. and Autz, H. M.. Tests on the Stress Distribution in Reinforced Panels. J. Aero. Sci., Vol. 3, p. 209.Google Scholar
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82. Ebner, H. and Köller, H.. On the Load Distribution in Longitudinally and Laterally Stiffened Shells. L.F.F. 15, p. 527.Google Scholar
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85. Portier, H.. The Riveting of Thin Sheets in Aeronautical Construction. Pub. Sci. et Tech. du Min. de l'air. B.S.7, No. 87.Google Scholar
1. Timoshenko, S.. The Theory of Elastic Stability (Book). McGraw Hill, 1936.Google Scholar
2. Southwell, R. V.. On the General Theory of Elastic Stability. Phil, Trans. A., Vol. 213, p. 187.Google Scholar
3. Donnell, L. H., Sechler, E. E. and Kármán, Th. V.. Survey of Problems of Thin- Walled Structures. C.I.T. Pub., No. 16.Google Scholar
4. Gerard, I. J.. Monocoque Construction. J.R.Ae.S., Vol. 41, p. 467.Google Scholar
5. Heck, O. S. and Ebner, H., Formulæ and Methods of Calculation of the Strength of Plate and Shell Structures in Aeroplane Construction. J.R.Ae.S., Vol. 40, p. 769.Google Scholar
6. Hoff, N. J.. Instability of Monocoque Structures in Pure Bending. T.R.Ae.S., Vol. 42, p. 291.Google Scholar
7. Wagner, H.. The Stress Distribution in Shell Bodies and Wings as an Equilibrium Problem. N.A.C.A. Techl. Mem., No. 817.Google Scholar
8. Ebner, H.. The Strength of Shell Bodies—Theory and Practice. N.A.C.A. Techl. Mem., No. 838.Google Scholar
9. Southwell, R. V.. On the Analysis of Experimental Observations in Problems of Elastic Stability. Proc. Roy. Soc. A., Vol. 135, p. 601.Google Scholar
10. Bryan, G. H.. On the Stability of a Plane Plate under Thrust. Proc. Lond. Math. Soc., Series 1, Vol. 22, p. 54.Google Scholar
11. Taylor, G. I.. The Buckling Load of a Rectangular Plate with Four Clamped Edges. Z.A.M.M. 13, p. 147.Google Scholar
12. Faxen, H.. Buckling of a Rectangular Plate. Z.A.M.M. 15, p. 268.Google Scholar
13. Weinstein, A.. On a Minimal Problem in the Theory of Elasticity. Jour. Lond. Math. Soc., Vol. 10, p. 184.Google Scholar
14. Trefftz, E.. The Estimation of the Buckling Load of a Rectangular Plate under Compression. Z.A.M.M. 15, p. 339.Google Scholar
15. Southwell, R. V. and Skan, S. W.. On the Stability under Shearing Forces of a Flat Elastic Strip. Proc. Roy. Soc. A., Vol. 105, p. 582.Google Scholar
16. Gough, H. J. and Cox, H. L.. Some Tests on the Stability of Thin Strip Material under Shearing Forces in the Plane of the Strip. Proc. Roy. Soc. A., Vol. 137, p. 145.Google Scholar
17. Aldous, C. W., Cox, H. L. and Gough, H. J.. The Strength of Panel Bracing. A.R.C. Techl. Rep. No. 3029 (unpublished).Google Scholar
18. Cox, H. L.. The Buckling of Thin Plates in Compression. A.R.C, R. & M. No. 1554.Google Scholar
19. Kármán, Th. V.. The Strength of Thin Plates in Compression. C.I.T. Pub. No. 13.Google Scholar
20. Schuman, L. and Back, G.. Strength of Rectangular Plates under Edge Compression. N.A.C.A. Techl. Rep. No. 356.Google Scholar
21. Sechler, E. E.. The Ultimate Strength of Thin Flat Sheets in Compression. C.I.T. Pub. No. 27.Google Scholar
22. Lahde, R. and Wagner, H.. Experimental Studies of the Effective Width of Buckled Sheet. L.F.F. 18, p. 214.Google Scholar
23. Marguerre, K.. The Effective Width of a Compressed Plate. L.F.F. 14, p. 121.Google Scholar
24. Wagner, H.. Plane Panel Frames of very Thin Sheet. Z.F.M. 20, p. 200 et seq.Google Scholar
25. Kuhn, P.. A Summary of Design Formulae for Beams having Thin Webs in Diagonal Tension. N.A.C.A. Techl. Note No. 469.Google Scholar
26. Atkin, E. H.. Stiffness in Stressed Skins. Aircraft Engineering, Vol. 8, p. 213.CrossRefGoogle Scholar
27. Schapitz, E.. Contributions to the Theory of the Incomplete Tension Bay. L.F.F. 14, p. 129.Google Scholar
28. Redshaw, S. C.. Elastic Stability of a Curved Plate under Axial Thrust. J.R.Ae.S., Vol. 42, p. 536.Google Scholar
29. Leggett, D. M. A.. The Elastic Stability of a Long Slightly Bent Rectangular Plate under Uniform Shear. Proc. Roy. Soc. A., Vol. 162, p. 62.Google Scholar
30. Sechler, E. E.. Preliminary Report on the Ultimate Compressive Strength of Curved Panels. C.I.T. Pub. No. 36.Google Scholar
31. Cox, H. L. and Clenshaw, W. J.. Compression Tests on Curved Panels of Thin Sheet Duralumin. A.R.C. Techl. Rep. No. 1576 (unpublished).Google Scholar
32. Marguerre, K.. On the Strength of Shells of Small Curvature. Proc. 5th Int. Cong. App. Mechanics. (See also Ref. 8.)Google Scholar
33. Smith, G. M.. Strength in Shear of Thin Curved Sheets of Alclad. N.A.C.A. Techl. Note No. 343.Google Scholar
34. Wagner, H. and Ballerstedt, W.. Fields of Tension Stress in Thin Plates, Initially Curved, under Shear Load. L.F.F. 12, p. 70.Google Scholar
35. Chwalla, E.. Collapse of Tubes under End Thrust. Z.A.M.M. 10, p. 72.Google Scholar
36. Donnell, L. H.. A New Theory for the Buckling of Thin Cylinders under Axial Compression'and Bending. A.S.M.E., AER-56-12.Google Scholar
37. Brazier, L. G.. The Flexure of Thin Cylindrical Shells and other Thin Sections. A.R.C, R. & M. No. 1081. (See also Ref. 2.)Google Scholar
38. Schwerin, E.. Torsional Stability of Thin-Walled Tubes. Z.A.M.M., Vol. 5, p. 235.Google Scholar
39. Donnell, L. H.. Stability of Thin-Walled Tubes under Torsion. N.A.C.A. Techl. Rep. 479.Google Scholar
40. Southwell, R. V.. On the Torsion of Conical Shells. Proc. Roy. Soc. A., Vol. 163, p. 337.Google Scholar
41. Robertson, A.. The Strength of Tubular Struts. Proc. Roy. Soc. A., Vol. 121, p. 558.Google Scholar
42. Lundquist, E. E.. Strength Tests of Duralumin Cylinders in Compression. N.A.C.A. Techl. Rep. No. 473.Google Scholar
43. Lundquist, E. E.. Strength Tests of Duralumin Cylinders in Pure Bending. N.A.C.A. Techl. Note No. 479.Google Scholar
44. Lundquist, E. E. and Burke, W. F.. Strength Tests of Thin-Walled Duralumin Cylinders of Elliptic Section. N.A.C.A. Techl. Note No. 527. (See also Ref. 4.)Google Scholar
45. Robertson, A. and Newport, A. J.. Torsion of Metal Tubes. III. Elastic Instability of Thin Tubes. A.R.C. Techl. Rep. No. 28.Google Scholar
46. Lundquist, E. E.. Strength Tests of Thin-Walled Duralumin Cylinders in Torsion. N.A.C.A. Techl. Note No. 427.Google Scholar
47. Bridget, F. J., Jerome, C. C. and Vosseller, A. B.. Some New Experiments, on Buckling of Thin-Wall Construction—Buckling under Combined Bending and Torsion. A.S.M.E., APM-56-6.Google Scholar
48. Lundquist, E. E.. Strength of Thin-Walled Duralumin Cylinders in Combined Transverse Shear and Bending. N.A.C.A. Techl. Note No. 523. (See also Ref. 4.)Google Scholar
49. Trayer, G. W. and March, H. W.. Elastic Instability of Members having Sections common in Aircraft Construction. N.A.C.A. Techl. Rep. No. 382Google Scholar
50. Wagner, H. and Pretschner, W.. Torsion and Buckling of Open Sections. N.A.C.A. Techl Mem. No. 784.Google Scholar
51. Parr, W. S. and Beakley, W. M.. An Investigation of Duralumin Channel Section Struts under Compression. J. Aero. Sci., Vol. 3, p. 21.Google Scholar
52. Lundquist, E. E.. The Compressive Strength of Duralumin Columns of Equal Angle Section. N.A.C.A. Techl. Note No. 413. (See also Ref. 47.)Google Scholar
53. Taylor, J. L.. Stability of a Monocoque in Compression. A.R.C, R. & M. 1679.Google Scholar
54. Cox, H. L. and Smith, H. E.. The Buckling of Grids of Stringers and Ribs. A.R.C. Techl. Rep. No. 2731. (To be published.)Google Scholar
55. Cox, H. L. and Clenshaw, W. J.. The Buckling of Combinations of Sheet and Stringers. A.R.C. Techl. Rep. No. 1586 (unpublished).Google Scholar
56. Lundquist, E. E.. Comparison of Three Methods for Calculating the Compressive Strength of Flat and Slightly Curved Sheet and Stringer Combinations. N.A.C.A. Techl. Note No. 455.Google Scholar
57. Newell, J. S. and Gale, W. H.. Report on Aircraft Materials Research at Massachusetts Institute of Technology, 1930–31.Google Scholar
58. Gerard, I. J. and Dickens, B. G.. Stressed Skin Structures. Compression Tests of Panels with Tubular Stiffeners. A.R.C, R. & M. No. 1830.Google Scholar
59. Ramberg, W., McPherson, A. E. and Levy, S.. Experimental Study of Sheet Stringer Panels under End Compression. Proc. 5th Int. Cong. App. Mech.Google Scholar
60. Dean, W. R.. The Elastic Stability of a Corrugated Plate. Proc. Roy. Soc. A., Vol. III , p. 144. (See also Ref. 53.)Google Scholar
61. Bergmann, S. and Reissner, H.. The Buckling of Corrugated Sheet in Shear. Z.F.M. 20, p. 475.Google Scholar
62. Seydel, E.. Buckling Tests of Panels of Corrugated Sheet. J.D.V.L. 1931, p. 233.Google Scholar
63. Greene, C. F. and Brown, C. G.. The Column Properties of Corrugated Aluminium Alloy Sheet. A.C.I.C. No. 699. (U.S. Army Air Corps.)Google Scholar
64. Djuan-Dschou, D.. The Buckling under Pressure of a Stiffened Cylindrical Shell. L.F.F. 9, p. 35. (See also Refs. 4, 6 and 8.)Google Scholar
65. Cox, H. L.. Stiffening of Webs containing Holes. A.R.C. Techl. Rep. No. 2158 (unpublished).Google Scholar
66. Gurney, C.. An Analysis of the Stresses in a Flat Plate with a Reinforced Circular Hole under Edge Forces. A.R.C, R. & M. No. 1834.Google Scholar
67. Schüssler, K.. Sheet Strip with Bedded Circular Holes in Shear. L.F.F. 11, p. 74.Google Scholar
68. Sezawa, K. and Kubo, K.. Stresses in a Plate with a Flanged Circular Hole. Tokyo Imp. Univ., Aero. Res. Inst., Rep. No. 84.Google Scholar
69. Mathar, J.. The Resistance to Shear and Buckling of Thin Plates with Lightening Holes. Proc. Aero. Inst., Aachen, 1929.Google Scholar
70. Cox, H. L., Smith, H. E. and Conway, C. G.. Diffusion of Concentrated Loads into Monocoque Structures. A.R.C, R. & M. No. 1780.Google Scholar
71. Duncan, W. J.. Diffusion of Load in Certain Sheet-Stringer Combinations. A.R.C, R. & M. No. 1825.Google Scholar
72. Smith, H. E.. Diffusion of Load in Sheet-Stringer Combinations having a Tapered Centre Stringer. A.R.C, R. & M. No. 1862.Google Scholar
73. Cox, H. L.. Diffusion of Concentrated Loads into Monocoque Structure. General Considerations with particular reference to Bending Load Distributions. A.R.C, R. & M. No. 1860.Google Scholar
74. Winny, H. F.. The Distribution of Stress in Monocoque Wings. A.R.C, R. & M. No. 1756.Google Scholar
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